On torsion points of formal groups over a ring of Witt vectors
Let k be a perfect field of characteristic \(p>0\). Let \(W=W(k)\) be the ring of Witt vectors over k and K its quotient field. Let \(\bar{\mathfrak m}\) be the maximal ideal of the ring of integers of an algebraic closure of K. For a one-dimensional formal group F defined over W of finite height h, denote by \(F_{p^ n}\) the set of elements of \(F(\bar{\mathfrak m})\) of order dividing \(p^ n\). Let \(m\geq 1\) and F be a formal group over W of height h, which corresponds to Honda's special element \(p+p^ mc_ 1T+...+p^ mc_{h-1}T^{h-1}+cT^ h\) \((c_ 1,...,c_{h-1},c\in W\), c invertible) [cf. \textit{T. Honda}, J. Math. Soc. Japan 22, 213-246 (1970; Zbl 0202.031)]. In this paper we explicitly describe the Galois extension \(K(F_{p^{m+1}})/K\). We also compute the ramification numbers of the extension. In particular our result gives an explicit description of \(K(F_ p^ 2)/K\) for all formal groups over W of height h.
scientific article; zbMATH DE number 3961839